Environmental Engineering Reference
In-Depth Information
Wake Turbulence
Mathematical models of wind turbine wake geometries are discussed in Chapter 6. In
addition to predicting reductions in steady wind speed, a model of the turbulence within
the wake of a wind turbine is important in the design of wind power stations. As noted ear-
lier in Equations (6-7), wake turbulence is a combination of
ambient
and
rotor-generated
components. The total turbulence in the wake has a fairly significant effect on its
crosswind size and downwind persistence. The turbulence intensity in the wake of a single
turbine has also been simulated in wind tunnels [
e.g.
Blackwell and Sheldahl 1977,
Boschloo 1977, Vermeulen 1978, Builtjes 1979]. However, there are various limitations
in all of the existing models in such areas as scaling, modeling of the interaction between
the wind and the turbine, and modeling of the boundary layer of the atmosphere.
One of the more complete field studies of the turbulent structure of a wind turbine
wake is that reported by Connell and George [1982]. The vertical-plane array at Clayton,
New Mexico, (Fig. 8-33) was employed to rotationally-sample the wake turbulence two dia-
meters downwind of the Mod-OA HAWT. The multiple-peak shape of the Lagrangian
spectra in the wake at this distance from the rotor was found to be similar to that upwind
of the turbine, for the same atmospheric stability. Turbulence was measured at 17 locations
in the wake and one location at the wake's edge. The
ambient turbulence intensity
(ratio
of turbulence to steady wind speed upwind of the rotor and outside the rotor wake) was
approximately 0.15. By deducting the ambient turbulence from the measured wake turbu-
lence, the pattern of
generated turbulence
shown in Figure 8-33 was obtained. The change
in turbulence is noted at each anemometer location in the array. Turbulence increased
within the main power-extraction region, while behind the tower and near the ground
turbulence stayed the same or decreased. Overall, the turbulence two-diameters downwind
of the turbine was increased about 0.24 m/s or 15 percent by the action of the rotor.
Turbulence Simulation
Simulated turbulence
is a computer-generated analog or digital signal which has
statistical properties equivalent to that of the turbulent wind. The resulting signal thus
resembles a time history of wind speed fluctuations. Turbulence simulation, when carried
out completely, can provide all three gust components as functions of time and position
in space for input into equations of motion (linear or non-linear) for structural dynamic
analysis. The output of these equations gives the dynamic response of the system in analog
or digital form, from which parameters such as the RMS response of the system, extremes
or peaks in response, and correlations between the response output and the turbulence input
can be calculated. Moreover, 3-dimensional turbulence simulation automatically includes
the effects of wind direction fluctuations on the power output of a HAWT.
Turbulence simulation procedures generally require considerable computer memory and
lengthy computational time. On the other hand, turbulence simulation provides the most
complete analysis of the effects of an unsteady, non-uniform wind field on the performance,
loads, and control of a wind turbine. In principle, one could simply use measured time
histories of wind speed and direction rather than simulated ones. However, this generally
results in lengthy and costly field projects with multi-anemometer arrays in the uncontrolled
environment provided by nature. Moreover, simulations can contain random or chance events
that do not necessarily occur during a specific measurement program, and statistical and at-
mospheric properties (such as power spectrum, turbulence intensity, stability, and surface
roughness) can be systematically varied to study their effects on the turbine.
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